The oriented graph complex revisited

TL;DR

This paper establishes a quasi-isomorphism between the Kontsevich graph complex and its oriented version, deepening understanding of their algebraic structures in the context of dg Lie algebras.

Contribution

It proves the quasi-isomorphism between the Kontsevich graph complex and its oriented counterpart, clarifying their relationship in dg Lie algebra theory.

Findings

Proved quasi-isomorphism between $GC_d^{2}$ and $OGC_{d+1}^2$

Enhanced understanding of the algebraic structures of graph complexes

Bridged the gap between oriented and non-oriented graph complexes

Abstract

We prove that the Kontsevich graph complex $GC_d^{2}$ and its oriented version $OGC_{d+1}^2$ are quasi-isomorphic as dg Lie algebras.